Question

the diagram shows graphs of y=1/2x+2 and 2y+2x=12. Use the diagram to solve the simultaneous equations

Answer 1

`\mathsf {(2.66, 3.33)}`

Step-by-step explanation:

`\textsf {Given :}`

`\mathsf {1) y = (1)/(2)x + 2}`

`\mathsf {2) 2y + 2x = 12} \implies \mathsf {y + x = 6} \implies \mathsf {y = -x + 6}`

`\mathsf{Solving :}`

`\textsf {Equating the values of y from both equations :}`

`\implies \mathsf {(1)/(2)x + 2 = -x + 6}`

`\implies \mathsf {(3)/(2)x = 4}`

`\implies \mathsf {3x = 8}`

`\implies \mathsf {x = (8)/(3) \implies {x = 2.66...}}`

`\textsf {Finding y :}`

`\implies \mathsf {y = -(8)/(3) + 6}`

`\implies \mathsf {y = (18 - 8)/(3)}`

`\implies \mathsf {y = (10)/(3)} \implies \mathsf {y = 3.33...}`

`\textsf {Graph of equations is attached below.}`

Answer 2

Answer: (2.67, 3.33)

Step-by-step explanation:

For the function y = 1/2x + 2

• y-intercept = (0, 2)

• x-intercept = (-4, 0)

`\hrulefill`

For the function 2y + 2x = 12

• y-intercept = (0, 6)

• x-intercept = (6, 0)

Draw lines through these coordinates to produce a straight linear graph.

Then see, where they intersect each other. Intersection point : (2.67, 3.33)